Future Generation Computer Systems
Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators
Artificial Intelligence Review
Parallel Computing with DNA: Toward the Anti-Universal Machine
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Programmable reconfiguration of Physarum machines
Natural Computing: an international journal
What is the region occupied by a set of points?
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Efficient convex-elastic net algorithm to solve the Euclideantraveling salesman problem
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Slime mould computes planar shapes
International Journal of Bio-Inspired Computation
Amoeba-based nonequilibrium neurocomputer utilizing fluctuations and instability
UC'07 Proceedings of the 6th international conference on Unconventional Computation
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The travelling salesman problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate solutions. Some methods take their inspiration from natural systems, extracting the salient features of such systems for use in classical computer algorithms. In this paper we demonstrate a simple unconventional computation method to approximate the Euclidean TSP using a virtual material approach. The morphological adaptation behaviour of the material emerges from the low-level interactions of a population of particles moving within a diffusive lattice. A `blob' of this material is placed over a set of data points projected into the lattice, representing TSP city locations, and the blob is reduced in size over time. As the blob shrinks it morphologically adapts to the configuration of the cities. The shrinkage process automatically stops when the blob no longer completely covers all cities. By manually tracing the perimeter of the blob a path between cities is elicited corresponding to a TSP tour. Over 10 runs on 20 randomly generated datasets consisting of 20 cities this simple and unguided method found tours with a mean average tour length of 6.41 % longer than the minimum tours computed by a TSP solver (mean best performance was 4.27 % longer and mean worst performance was 9.22 % longer). We examine the insertion mechanism by which the blob constructs a tour, note some properties and limitations of its performance, and discuss the relationship between the blob TSP and proximity graphs which group points on the plane. The method is notable for its simplicity, novelty and the spatially represented mechanical mode of its operation. We discuss similarities between this method and previously suggested models of human performance on the TSP and suggest possibilities for further improvement.